Oversampling Analog to Digital Converters

226 Pages·2008·3.22 MB·English

Oversampling Analog to Digital Converters
21st International Conference on VLSI Design, Hyderabad
Shanthi Pavan
Nagendra Krishnapura
DepartmentofElectricalEngineering
IndianInstituteofTechnology,Madras
Chennai,600036,India
4 January 2008
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Outline
Introduction to sampling and quantization
Quantizationnoisespectraldensity
Oversampling
Noiseshaping-∆Σmodulation
High order multi bit ∆Σ modulators
Stability of ∆Σ A/D converters
Implementation of ∆Σ A/D converters
Loopfilterdesign
Multibitquantizerdesign
Excessdelaycompensation
Clockjittereffects
Mitigation of feedback DAC mismatch
Dynamicelementmatching
DACcalibration
Case study
15bitcontinuous-time∆ΣADCfordigitalaudio 2
ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Signal processing systems
Sensor(s) Digital Processing Actuator(s)
. . .
DSP
. . . ...0100011011...
. . .
Continuous-time Discrete -time Continuous-time
Continuous-amplitude Discrete -amplitude Continuous-amplitude
Interface Electronics
(Signal Conditioning)
(A-D and D-A Conversion)
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Signal processing systems
Natural world: continuous-time analog signals
Storage and processing: discrete-time digital signals
Data conversion circuits interface between the two
Wide variety of precision and speed
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Continuous time signals
Continuous−time analog signal
7V
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2V
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V
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0
0
T 2T 3T 4T 5T 6T 7T 8T 9T 10T
s s s s s s s s s s
Signals defined for all t
Signals can take any value in a given range
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Discrete time signals
Discrete time signal
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0
0 1 2 3 4 5 6 7 8 9 10
Signals defined for discrete instants n
Signals can take any value in a given range
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Digital signals
Sampled quantized(digital) signal
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0
0 1 2 3 4 5 6 7 8 9 10
Signals defined for discrete instants n
Signals can take discrete values kV
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Sampling and quantization
A segment of a continuous-time signal has an infinite
number of points of infinite precision
Discretization of time(sampling) and
amplitude(quantization) results in a finite number of points
of finite precision
Sampling and quantization = Analog to digital conversion
Errors in the process?
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Signals in time and frequency domains
Continuous time signal x (t)
ct
Frequency domain representation using its Fourier
transform X (f)
ct
∞
X (f) = x (t)exp( j2πft)dt
ct ct
Z −
−∞
Discrete time signal x [n]
d
Frequency domain representation using its Fourier
transform X (ν)
d
∞
X [ν] = x [n]exp( j2πνn)
d d
−
n=X
−∞
X [ν] periodic with a period of 1
d 9
ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters
Signals in time and frequency domains
Continuous−time analog signal Fourier transform of a continuous−time signal
7V
LSB
6V
LSB
5VLSB 1.0
4V
LSB
3V
LSB
2V
LSB
V
LSB
f
b
0 0
0 Ts 2Ts 3Ts 4Ts 5Ts 6Ts 7Ts 8Ts 9Ts 10Ts 0 fs 2fs
∞
X (f) = x (t)exp( j2πft)dt
ct ct
Z −
−∞
Signal bandwidth f : X (f) = 0 for f > f
b ct b
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ShanthiPavan NagendraKrishnapura OversamplingAnalogtoDigitalConverters